NURBS Sweep

Dependencies

This node can optionally use Geomdl library; it can also optionally use FreeCAD libraries.

Functionality

This node generates a NURBS Surface object by sweeping (extruding) one NURBS curve (called “profile”) along another NURBS curve (called “path”).

Several profile curves can be also used; in this case the resulting surface will be interpolated between them. If several profile curves are used, the user can provide specific values of path’s curve T parameter, at which profile curves must be placed; otherwise, the node will place them automatically evenly along T parameter of the path curve.

It is supposed that initially the provided profile curve(s) are placed near global origin. If profile curves passes through global origin, then the resulting surface will go through the path curve.

The node works by placing several copies of profile curve along the path curve, and then lofting (skinning) between them. If several profile curves are used, then the node interpolates between them and places these interpolated curves along the path curve.

Several algorithms to calculate rotation of profile curve are available. In simplest cases, all of them will give very similar results. In more complex cases, results will be very different. Different algorithms give best results in different cases:

• “Frenet” or “Zero-Twist” algorithms give very good results in case when extrusion curve has non-zero curvature in all points. If the extrusion curve has zero curvature points, or, even worse, it has straight segments, these algorithms will either make “flipping” surface, or give an error.

• “Householder”, “Tracking” and “Rotation difference” algorithms are “curve-agnostic”, they work independently of curve by itself, depending only on tangent direction. They give “good enough” result (at least, without errors or sudden flips) for all extrusion curves, but may make twisted surfaces in some special cases.

• “Track normal” algorithm is supposed to give good results without twisting for all extrusion curves. It will give better results with higher values of “resolution” parameter, but that may be slow.

• “Specified Y” algorithm selects rotation so that it satisfies two conditions: 1) profile plane is perpendicular to curve’s tangent vector, and 2) local Y axis of the profile curve points in general direction of “Normal” vector, provided by the user. This algorithm is supposed to give good results for planar or almost planar path curves. The resulting surface may have twists in places where original curve’s tangent vector is parallel to offset operation plane’s normal (i.e. tangent is perpendicular to offset operation plane).

This node is similar to “Extrude Curve along Curve” node; differences are:

• “NURBS Sweep” can work with NURBS and NURBS-like curves only, while “Extrude Curve along Curve” works with arbitrary (e.g. formula-specified) Curve objects.

• “NURBS Sweep” node always generates a NURBS surface; for such surface, some specific API methods can be applied; such surface can be saved in some file format, which understands only NURBS (at the moment, see “NURBS to JSON” node; later, nodes to save NURBS in some industry-used formats can appear).

• “NURBS Sweep” supports several profile curves.

Another similar node is “NURBS Birail”, that one works with two path curves instead of one.

At the moment, this node can effectively work with the following types of curves:

• NURBS curves

• Bezier curves

• Cubic splines

• Polylines

• Circular arcs

• Line segments

Some nodes, that output complex curves composed from simple curves (for example, “Rounded rectangle”), have NURBS output parameter; when it is checked, such nodes output NURBS curves, so “NURBS Sweep” can work with them.

Inputs

This node has the following inputs:

• Path. The path curve, along which profile curves must be swept. This input is mandatory.

• Profile. Profile curve or curves. The node can work with one profile curve per path curve, or list of profile curves per path curve. This input is mandatory.

• VSections. Number of copies of profile curve (or interpolated curves, if several profile curves are used) the node will generate for lofting. This will be equal to number of control points of the resulting surface along it’s V direction. Bigger values usually correspond to better precision of sweeping procedure; but too high numbers can cause weird results or be too slow. The default value is 10.

• V. Values of V parameter (i.e. path curve’s T parameter), at which profile curves must be placed for lofting. This input is available and mandatory if Explicit V Values parameter is checked. The node expects number of values in this input equal to number of profile curves. For one profile curve, this input has no meaning.

• Resolution. Number of samples for Zero-Twist or Track normal rotation algorithm calculation. The more the number is, the more precise the calculation is, but the slower. The default value is 50. This input is only available when Algorithm parameter is set to Zero-Twist or Track normal.

• Normal. Orientation vector. This input is available only when Algorithm parameter is set to Specified Y. The default value is (0, 1, 0).

Parameters

This node has the following parameters:

• Implementation. This defines the implementation of NURBS mathematics to be used. The available options are:

  • Geomdl. Use Geomdl library. This option is available only when Geomdl package is installed.

  • Sverchok. Use built-in Sverchok implementation.

  • FreCAD. Use FreeCAD libraries. This option is available only when FreeCAD libraries are installed.

  In general, built-in implementation should be faster; but Geomdl implementation is better tested. The default option is Geomdl, when it is available; otherwise, built-in implementation is used.

• Algorithm. Algorithm of calculating the orientation of profile curves with relation to path curve. The available options are:

  • None. Do not rotate the profile curve, just extrude it as it is. This mode is the default one.

  • Frenet. Rotate the profile curve according to Frenet frame of the extrusion curve.

  • Zero-Twist. Rotate the profile curve according to “zero-twist” frame of the extrusion curve.

  • Householder: calculate rotation by using Householder’s reflection matrix (see Wikipedia article).

  • Tracking: use the same algorithm as in Blender’s “TrackTo” kinematic constraint. This node currently always uses X as the Up axis.

  • Rotation difference: calculate rotation as rotation difference between two vectors.

  • Track normal: try to maintain constant normal direction by tracking it along the curve.

• Explicit V Values. If checked, then the user has the ability to provide values of path curve’s parameter values, at which the provided path curves must be placed; otherwise, the node will calculate these parameters automatically (evenly). This parameter has no meaning if there is only one profile curve.

• U Knots. This parameter is available in the N panel only. This defines how the node will modify input curves in order to make them use exactly the same knot vectors. Available options are:

  • Unify. Additional knots will be inserted for each curve in places where other curves have knots.

  • Average. Calculate knot vector by averaging knot vectors of the input curves. This can work only when input curves have the same number of control points.

  Unify option often generates a lot of additional control points for the resulting surface; it is more universal, and more precise in many cases. Average mode does not create additional control points, and so it works faster, and any following nodes working with the generated surface will work faster; but Average mode is less universal, and in many cases it gives less precise interpolations. The default value is Unify.

• Metric. This parameter is available in the N panel only. Distance type used for interpolation along V direction. The available values are:

  • Manhattan

  • Euclidean

  • Points (just number of points from the beginning)

  • Chebyshev

  • Centripetal (square root of Euclidean distance).

  The default option is Euclidean.

Outputs

This node has the following outputs:

• Surface. The generated NURBS surface.

• AllProfiles. Curves that were actually used to construct the surface. These are the curves provided in the Profile input, placed at their places along path curve and interpolated (if several profiles were used).

• VCurves. Curves along V direction of the surface, which were used to calculate surface’s control points during skinning process.

Examples of usage

One Profile curve:

Two Profile curves:

Three Profile curves: